The 29-year-old, currently with Colombia at the Copa America in Chile, scored four goals in 29 appearances for Manchester United last season.
United rejected the chance to sign him for a reported £43.2m but now the Premier League champions have moved in.
Details of an agreement that would secure Falcao a second season in the top flight are still being finalised.
On Thursday, Mourinho responded to reports linking Chelsea with a move for Falcao by saying: "It hurts me that people in England think that the real Falcao is the one we saw at Manchester United."
Speaking to DirecTV Sports, the Portuguese added: "If I can help Falcao reach his level again, I will do it."
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